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    Re: Lunar Distance in Wikipedia
    From: George Huxtable
    Date: 2007 Aug 2, 11:53 +0100

    Renee wrote-
    | http://en.wikipedia.org/wiki/Lunar_distance_%28navigation%29
    | I have made a major rewrite, partly from Paul's suggestions, partly from
    | not-half-bad summary of lunars in the article on Celestial Navigation
    | (http://en.wikipedia.org/wiki/Celestial_navigation#Lunar_distance), and
    | partly from my own ideas.  Sorry about that last part.  I don't know when
    | the Nautical Almanac added the planets to the lunar distance tables, but I
    | am certain George can get back to us after he completes his article for
    | "Navigation News".
    | I struck out the "Theory" section and subsumed the "practice" section into
    | the "Method" introductory paragraph.
    | I think Wikipedia now has the bare bones of a decent article.
    | We can leave it as-is and suggest further outside-of-wikipedia reading on
    | the subject (web pages AND books).
    | Or we can add as much information as all of you lunar experts can supply.
    | Explain the size of the error introduced if parallax is not corrected for.
    | Define "clearing".  Describe (in 100 words or less) the difference between
    | the method of lunar distance, as originally presented by Maskeleyne, and
    | "new lunars" recently discussed on this list.  Fill in useful bits of
    | history (cross-reference the longitude article whenever possible).  Add
    | citations (just place them in-line -- citation experts will rush in to
    | them into footnotes).  If you how an encyclopedia article is supposed to
    | turn out, you get the gist of the style guidelines.  Just typing in some
    | text is easy.  You don't even have to create an account.
    Renee has tempted me to take a look at the revamped article. And indeed,
    it's a lot better. Still, there are one or two suggestions to offer, some
    errors to fix, additions to make. I wonder if Renee is prepared to have
    another go, rather than having several of us poking fingers into the pie. I
    will append a few suggested alterations, for Renee and others to shoot down
    or tinker with as they see fit. All the suggestions below are rather
    Lunar distance (navigation)
    From Wikipedia, the free encyclopedia
    In celestial navigation, lunar distance is the angle between the Moon and
    another celestial body. A navigator can use a lunar distance (also called a
    lunar) and a nautical almanac to calculate Greenwich time. The navigator can
    then determine longitude without a chronometer.
    =====That's good, I think. Nice and concise.
    [edit] Why Measure Lunar Distances?
    In Celestial navigation, precise knowledge of the time at Greenwich and the
    positions of one or more celestial objects are combined with careful
    observations to calculate latitude and longitude. [1] But accurate Greenwich
    time from chronometers was not generally available at sea until well into
    the 19th century. [2] [3] For nearly one hundred years (from about 1767
    until 1850), the method of lunar distances was used to determine longitude
    at the time of the lunar observation. If a chronometer is available,
    longitude information can also be used to check and correct chronometer
    =====Well, the last sentence is misleading. To correct a chronometer, you
    don't need longitude (which would call for an observation for local time).
    Just Greenwich Time, directly from the lunar, is all that's needed. And that
    shows up the problem with the previous sentence, because the lunar distance
    determines Greenwich Time, not longitude. It's just one step in determining
    longitude; but a major step. The next step is determining the local time.
    Only then do you have longitude.
    So my suggestion is to change the last two sentences into something like-
    "For nearly one hundred years (from about 1767 until 1850), mariners lacking
    a chronometer would use the method of lunar distances to determine Greenwich
    Time, an important step in finding their longitude. For those with a
    chronometer, its reading could be checked and corrected from a lunar
    determination of Greenwich Time [2]."
    Does that make sense?
    [edit] Method
    The method relies on the relatively quick movement of the moon across the
    background sky. It completes a circuit of 360 degrees in 27.3 days, about
    1/2 degree per hour,[1] approximately equal to the angular diameter of the
    moon. The navigator precisely measures the angle between the moon and a body
    like the sun or a selected group of stars lying along the ecliptic. At that
    moment in time, anyone on the surface of the earth who can see the moon,
    would observe the same angle (corrected for errors). Certain almanacs list
    lunar distances in tables. The navigator can find the angle he or she
    measured, and thus know the time at Greenwich. Knowing Greenwich time and
    local time, the navigator can work out longitude.
    =======Can I suggest some changes here, for Renee to consider? Try this-
    The method relies on the relatively quick movement of the Moon across the
    background sky, completing  a circuit of 360 degrees in 27.3 days. In an
    hour, then, it will move about half a degree [1], roughly its own diameter,
    with respect to the background stars, and the Sun.  Using a sextant, the
    navigator precisely measures the angle, slantwise across the sky, between
    the Moon and another body. That could be the Sun or one of a selected group
    of bright stars lying near the ecliptic, close to the Moon's path. At that
    same moment, anyone on the surface of the Earth, who could see those same
    two bodies, would observe the same angle between them (after important
    corrections had been made, as described below). Until the early years of the
    20th century, almanacs listed predicted lunar distances to those bodies in
    tables, in relation to Greenwich Time. By comparing his corrected lunar
    distance with such a table, the mariner obtained the Greenwich Time of that
    Local time was usually determined by a sextant observation of the altitude
    of the Sun [4] above the horizon [1], at morning or evening ; a star, rising
    or falling, could also be used. Then, longitude (from Greenwich) was readily
    calculated from the difference between local time and Greenwich Time, at 15
    degrees per hour.
    =========Above, I've left those numbered citations in, without being sure
    how relevant they are to the text, without having those editions to hand to
    correspond with those page numbers. Would it be better to cross-refer to
    other entries within Wikipedia, where they are relevant?
    I think the section below is an important one, and I have expanded it
    considerably. It's not really more than a first-draft, but what do others
    [edit] Errors and corrections.
    A lunar distance changes with time at a rate of roughly half a degree, or 30
    arc-minutes, in an hour. An error of just one arc-minute, then, will give
    rise to an error of about 2 minutes in Greenwich Time. The Earth spins at 15
    degrees per hour, so that would lead to an error of half a degree, or 30
    arc-minutes, in the resulting longitude; near the Equator; that corresponds
    to 30 miles. So lunar distance can never be a precise way to determine
    longitude, but nevertheless, to a navigator approaching a continent from the
    ocean, even such a rough figure was of great value. Thirty minutes in
    longitude was the target set by the famous Longitude Prize, which was won in
    the end, not by the lunar method, but by Harrison with his chronometer.
    In the early days of lunars, predictions of the Moon's position were good
    only to half an arc-minute, so to obtain the required overall precision of
    one arc-minute, only half a minute could be allowed for errors in measuring
    the lunar distance, and in calculation, combined. The best sextants could
    indicate angle to one-sixth of a minute, but in practice at sea, actual
    errors were somewhat larger, good observers typically achieving overall
    accuracy within half a minute in favourable conditions. From the unstable
    deck of a small vessel, in bad weather, with the sextant elevated and tilted
    at an awkward angle to get both objects simultaneously in view in its small
    mirrors, and with much of the sky obscured by square sails, it became a
    severe test of a navigator's skill.
    Almanac tables predicted lunar distances between the centre of the Moon and
    the centre of the Sun, as would be seen by an imaginary observer placed at
    the centre of a transparent Earth. In an observation, the centre of the Moon
    can not be estimated with sufficient accuracy. Instead lunar distances were
    always measured to the sharply lit, outer edge ("limb") of the Moon, and an
    allowance then made, from the almanac, for the Moon's "semidiameter", for
    that day; and similarly for the Sun. That was the first step in the
    correction process.
    The second step, always referred to as "clearing" a lunar, was in allowing
    for the effects of parallax and atmospheric refraction on the observed lunar
    distance. These vary, depending on the altitudes of the two bodies.
    Parallax, which changes the apparent position in the sky depending on the
    perspective of just where it's seen from, is especially important for the
    Moon, because it is so close to the Earth. It can shift the Moon's position
    by up to a whole degree, and has to be corrected for with great precision.
    In most celestial observations, measuring up from the horizon, correction
    for these effects would be a simple addition or subtraction. Not so for a
    lunar, however, because of its skewed angle. Instead, additional
    measurements are made of altitudes of the two bodies, close to the same
    moment as that of the lunar distance, high accuracy not being needed for
    those altitudes, in themselves. Great precision was required in the
    resulting calculations, however, which called for five-figure log tables of
    trig functions.
    In some circumstances, that additional measurement of Sun or star altitude
    could also be used to derive local time, bypassing the need for a separate
    I will leave it at that for now, to see what reactions follow. Some
    tinkering with the history section might be worthwhile, and may appeal to
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    To post to this group, send email to NavList@fer3.com
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